Maple 9 Learning Guide - Maplesoft

234 • Chapter 7: Solving Calculus Problems> ApproximateInt( f(x), x=0..4*Pi, method=left, partition=6,> output=animation, iterations=7);An Approximation of the Integral off(x) = 1/2+sin(x)on the Interval [0, 4*Pi]Using a Left-endpoint Riemann SumApproximate Value: 6.283185307An Approximation of the Integral off(x) = 1/2+sin(x)on the Interval [0, 4*Pi]Using a Left-endpoint Riemann SumApproximate Value: 6.283185307An Approximation of the Integral off(x) = 1/2+sin(x)on the Interval [0, 4*Pi]Using a Left-endpoint Riemann SumApproximate Value: 6.283185307An Approximation of the Integral off(x) = 1/2+sin(x)on the Interval [0, 4*Pi]Using a Left-endpoint Riemann SumApproximate Value: 6.2831853071.51.51.51.511110.50.50.50.502 4 6 8 10 12x02 4 6 8 10 12x02 4 6 8 10 12x02 4 6 8 10 12x–0.5–0.5–0.5–0.5–1Area: 6.283185309–1Area: 6.283185308–1Area: 6.283185308–1Area: 6.283185311f(x)f(x)f(x)f(x)An Approximation of the Integral off(x) = 1/2+sin(x)on the Interval [0, 4*Pi]Using a Left-endpoint Riemann SumApproximate Value: 6.283185307An Approximation of the Integral off(x) = 1/2+sin(x)on the Interval [0, 4*Pi]Using a Left-endpoint Riemann SumApproximate Value: 6.283185307An Approximation of the Integral off(x) = 1/2+sin(x)on the Interval [0, 4*Pi]Using a Left-endpoint Riemann SumApproximate Value: 6.2831853071.51.51.51110.50.50.502 4 6 8 10 12x02 4 6 8 10 12x02 4 6 8 10 12x–0.5–0.5–0.5–1Area: 6.283185308–1Area: 6.283185309–1Area: 6.283185309f(x)f(x)f(x)In the limit, as the number of boxes tends to infinity, you obtain thedefinite integral.> Int( f(x), x=0..10 );∫ 101+ sin(x) dx0 2The value of the integral is> value( % );−cos(10) + 6and in floating-point numbers, this value is approximately> evalf( % );6.839071529The indefinite integral of f is> Int( f(x), x );